Stochastic equations with the eyes of a physicist. (Q2782029)

The book treats the statistical theory of dynamical and wave systems with fluctuating random parameters. Such systems can be described by ODEs, PDEs, integral or integro-differential equations. The goal of the monograph is to develop the unified functional approach for the analysis of these systems and to obtain explicit formulae for those statistical characteristics. The main focus is given to systems with Gaussian random parameters. NEWLINENEWLINENEWLINEThe book consists of five parts. Part I is introductory. Some typical physical problems (oscillator with random frequency, Helmholtz and Navier-Stokes equations etc.) are considered. Part II contains the general theory of statistical analysis of dynamical systems with fluctuating parameters. Particular systems are considered to illustrate the general theory. Part III treats asymptotic methods: approximations of temporarily \(\delta\)-correlated Gaussian process (field) and diffusive approximation. Part IV applies the general theory to study scattering and localization of waves in random media, turbulence, statistical hydrodynamics etc. The last Part V consists of three appendices devoted to the basics of variational analysis, fundamental solutions of wave equations, and the imbedding method in statistical boundary-value problems. The book is richly illustrated. Its bibliography contains 227 entries.